On some bivariate interpolation procedures

Abstract

In an important paper published in 1966 by the first author [10] a very general interpolation formula for univariate functions, which includes, as special cases, the classical interpolation formulae of Lagrange, Newton, Taylor and Hermite was introduced and investigated. The purpose of the present paper is to extend that formula to the two-dimensional case. The remainders are expressed by means of partial divided differences and derivatives.